Some new applications of the quantum-difference operator on subclasses of multivalent $q$-starlike and $q$-convex functions associated with the Cardioid domain

In this study, we consider the quantum difference operator to define new subclasses of multivalent $q$-starlike and $q$-convex functions associated with the cardioid domain. We investigate a number of interesting problems for functions that belong to these newly defined classes, such as bounds for the first two Taylor-Maclaurin coefficients, estimates for the Fekete-Szeg ö type functional, and coefficient inequalities. The important point of this article is that all the bounds that we have investigated are sharp. Many well-known corollaries are also presented to demonstrate the relationship between prior studies and the results of this article.